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<h1 class="reftitle">reachableSet</h1>
<h2>Purpose</h2>
<p>Computes forward or backwards reachable sets</p>
<h2>Syntax</h2>
<pre class="synopsis">[S, SN] = system.reachableSet('X', X, 'U', U, 'N', N, 'direction', ['forward'|'backwards'])</pre>
<h2>Description</h2>
<p></p> 
    
      <tt>S = system.reachableSet('X', X, 'U', U, 'direction',
    'forward')</tt> computes the forward reachable set for an LTI
    system, i.e.,
    <p class="programlistingindent"><img src="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset4.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset4.png"></p>

    
      <tt>S = system.reachableSet('X', X, 'U', U, 'direction', 'backward')</tt> 
    computes the backward reachable set, i.e.,
    <p class="programlistingindent"><img src="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset5.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset5.png"></p>
		
    If <tt>X</tt> and/or <tt>U</tt> are not given, the constraints are
    extracted from state and input constraints. If <tt>direction</tt>
    is not specified, <tt>direction='forward'</tt> is assumed.<br><br>
		
    This function supports autonomous systems as well.
  <h2>Input Arguments</h2>
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<td><tt>X</tt></td>
<td>
<p></p>Polyhedron defining state constraints (optional)<p>
	    		Class: <tt>polyhedron</tt></p>
</td>
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<tr valign="top">
<td><tt>U</tt></td>
<td>
<p></p>Polyhedron defining input constraints (optional)<p>
	    		Class: <tt>polyhedron</tt></p>
</td>
</tr>
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<td><tt>direction</tt></td>
<td>
<p></p>Flag to switch between forward and backwards reachability.<p>
	    		Class: <tt>char</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>N</tt></td>
<td>
<p></p>Number of steps (defaults to 1).<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
</tbody>
</table>
<h2>Output Arguments</h2>
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<td><tt>S</tt></td>
<td>
<p></p>Set of states reachable in <img src="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset1.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset1.png"> steps.<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
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<td><tt>SN</tt></td>
<td>
<p></p>Set of states reachable at each step.<p>
	    		Class: <tt>cell</tt></p>
</td>
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<h2>Example(s)</h2>
<h3>Example 
				1</h3>Define a 2D LTI system <img src="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset2.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset2.png">.<pre class="programlisting">sys = LTISystem('A', [1 1; 0 1], 'B', [1; 0.5]);</pre>
<pre class="programlisting"></pre>Specify domain of states and inputs<pre class="programlisting">X = Polyhedron('lb', [-1; -1], 'ub', [1; 1]);
    U = Polyhedron('lb', -1, 'ub', 1);
    </pre>
<pre class="programlisting"></pre>Compute forward reachable set.<pre class="programlisting">S = sys.reachableSet('X', X, 'U', U, 'direction', 'forward');</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">S.plot()</pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset_img_1.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset_img_1.png" width="60%"></p>
<h3>Example 
				2</h3>Define a 2D LTI system <img src="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset3.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset3.png">.<pre class="programlisting">sys = LTISystem('A', [1 1; 0 1], 'B', [1; 0.5]);</pre>
<pre class="programlisting"></pre>Specify domain of states and inputs<pre class="programlisting">X = Polyhedron('lb', [-1; -1], 'ub', [1; 1]);
    U = Polyhedron('lb', -1, 'ub', 1);
    </pre>
<pre class="programlisting"></pre>Compute the backward reachable set.<pre class="programlisting">S = sys.reachableSet('X', X, 'U', U, 'direction','backward');</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">S.plot()</pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset_img_2.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/reachableset_img_2.png" width="60%"></p>
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<br><p>©  <b>2003-2013</b>     Michal Kvasnica: STU Bratislava,    <a href="mailto:michal.kvasnica@stuba.sk">michal.kvasnica@stuba.sk</a></p>
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